Brining rack of lamb

I am making a crown rack of lamb tomorrow, and today to prep I plan on getting some of the trimming done. I went to a new butcher this time around and sadly they left the extra layer of fat on the meat side of the racks which I want to remove (i'm a bit angry considering I paid about $30 extra because of that layer of fat).

Anyways - I know lamb doesn't have a lot of extra moisture of intramuscular fat. So, it would seem like it is a natural candidate for wet or dry brining. However despite a ton of searching I can't find anything referencing brining racks or crown racks of lamb. I know the amount of actual meat on each bone isn't huge so I am concerned about over-brining or washing out the delicate flavor of the lamb.

So, is brining lamb not a thing? Is there a specific reason to brine or not to brine lamb?